。
She monopolized her parents' affection.
Literal
She [topic-は] parents [possessive-の] affection [object-を] monopolized.
独占する (どくせんする, 'to monopolize') is a Sino-Japanese suru-verb used here for emotional territory. 愛情 (あいじょう, 'affection, love') is a formal word for familial or romantic love. The sentence implies she either was an only child or actively excluded siblings.