Category	Rules of Registration of the Data
Child’s age	We distinguished between children younger than 14 and registered the cases in which all the children in the family were younger than 14, children of 14 years or more and registered the cases in which all the children of the family were aged 14 years or older, and the third sub-category in which there were children that were both younger and older than 14, where we registered all the other cases.
Child’s behaviors—other risky behaviors	Other risky behaviors (home absenteeism, self-harm) were some of the changes in a child’s behavior identified by some of the child carers. We distinguished between the presence of the other risky behaviors, where we registered the cases in which the child carer mentioned home absenteeism and/or self-harm and the absence of other risky behaviors, where we registered all the other cases.
Child’s behavior—school absenteeism	School absenteeism was one of the behaviors that were mentioned by some of the child carers. We distinguished between the presence of the school absenteeism behavior, where we registered the cases in which the child carer mentioned school absenteeism or school abandoning, and the absence of this behavior, where we registered all the other cases.
Child’s emotional experience after the migration of the parent	We distinguished between pleasant and unpleasant emotional experiences of the children after the migration of their parent(s) or no change, as described by the child carer. We did not encounter cases where some of the children experienced a pleasant emotional experience and the other children of the same family experienced an unpleasant emotional experience.
Unpleasant emotional experience	When analyzing the data, the following two sub-categories emerged: (1) Short-term and low-intensity unpleasant emotional experience, which included registrations of the cases where the child care mentioned that the emotional states lasted for minutes, hours, and days, or were passing emotional experiences; a low intensity of the unpleasant emotional experience was explicitly mentioned; the children had high-intensity feelings but had overcome them at the time of the interview. (2) The children had long-term and high-intensity unpleasant emotional experience, which included the cases where the child carer mentioned that the emotional state seemed to be permanent or explicitly emphasized the unpleasant emotional state of the child. We did not encounter cases where some of the children experienced a short-term unpleasant emotional experience and the other children of the same family experienced a long-term unpleasant emotional experience.
Emotional closeness between the child and the guardian prior to the migration	We distinguished between poor emotional closeness, where we registered the cases in which the guardian explicitly mentioned not being close to the child or having a conflicting relationship with them, and good emotional closeness between the child and the child carer, where we registered all the other cases.
Emotional closeness between the child and the guardian after the migration	We distinguished between poor emotional closeness, where we registered the cases in which the guardian explicitly mentioned not being close to the child or having a conflicting relationship with them, and good emotional closeness between the child and the child carer, where we registered all the other cases.
Emotional closeness between the child and the migrated parent(s) prior to their migration	We distinguished between poor emotional closeness, where we registered the cases in which the child carer explicitly mentioned that the migrated parent(s) was/were not close to the child or had a conflicting relationship with them prior to their migration, and good emotional closeness, where we registered all the other cases.
Emotional support role performance of the migrated parent(s)	Consisted of emotional closeness between the child and the migrated parent(s) after their migration, frequency of communication through ICT, and frequency of visits. When the emotional closeness between the child and the migrating parent(s) after their migration was good, the frequency of communication through ICT was multiple times a week, and the frequency of visits was at least once a year, the case was registered as good emotional support. When the emotional closeness between the child and the migrating parent(s) after their migration was poor, the frequency of communication through ICT was once a week or less, and the frequency of visits was less than once a year, the case was registered as poor emotional support. All the other cases were registered as moderate emotional support.
Emotional closeness between the child and the migrated parent(s) after their migration	We distinguished between poor emotional closeness, where we registered the cases in which the child carer mentioned a poor emotional connection, the lack of reciprocity, or the existence of a conflict between the child and the migrating parent(s), and good emotional closeness between the child and the guardian, where we registered all the other cases.
Frequency of communication through ICT	We distinguished between the following two subcategories: multiple times a week and once a week or less.
Frequency of visits	We distinguished between the following two subcategories: at least once a year and less than once a year.
Migrated parent(s) as a constant income provider	We distinguished between the following two subcategories: cases in which the migrated parent(s) was (were) a constant income provider(s), even if the income provided was sometimes in a small amount and did not suffice for the month-to-month expenses, and cases in which the migrating parent(s) was (were) not a constant income provider(s), occasionally sending money to the family.
Migration motive	The motive identified in all cases was material support for the family, especially for the children. We also identified the dissolution of the conjugal couple, complementary to material support in one of the cases; therefore, in order to create mutually exclusive sub-categories, we registered material support as one category and material support and dissolution of the conjugal couple as the second sub-category.
The fulfillment of the basic needs (food, clothes, shoes, heating)	We distinguished between the cases in which the basic needs of the children (food, clothes, shoes, heating) were fulfilled and the cases in which the basic needs of the children were not fulfilled.
The migrated parent	The following three types of cases emerged: the migrated parent was the mother, the father, or both parents migrated.
The guardian/child carer	The following two types of cases emerged: the cases in which the child carer was one of the parents and the case in which the child carers were the grandparents.