zuerkennen
to award
To grant and give someone something (e.g., a prize, a right, or a sum of money) in an official or legal procedure.
Das Gericht hat der Mutter das alleinige Sorgerecht zuerkannt.
The court awarded the mother sole custody.

to award / attribute
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to award
To grant and give someone something (e.g., a prize, a right, or a sum of money) in an official or legal procedure.
Das Gericht hat der Mutter das alleinige Sorgerecht zuerkannt.
The court awarded the mother sole custody.

'Zuerkennen' (to award/attribute) is a separable verb. In a main clause in the present or simple past tense, the prefix 'zu' goes at the end of the sentence. In subordinate clauses and in the infinitive, the verb stays together.
Das Gericht erkennt ihm ein Schmerzensgeld zu.
The court awards him compensation for pain and suffering.
This verb requires a fixed structure: the person who receives something is in the dative, and the thing that is awarded or granted is in the accusative. The pattern is: jemandem (dative) etwas (accusative) zuerkennen.
Man erkannte der Autorin (Dativ) den Nobelpreis (Akkusativ) zu.
The author (dative) was awarded the Nobel Prize (accusative).
In the legal or official meaning, 'zuerkennen' (to award/grant) is often combined with rights or sums of money. Common objects are 'einen Preis' (a prize), 'ein Recht' (a right), 'das Sorgerecht' (custody), or 'Schadensersatz' (damages).
Der Jury war es eine Ehre, ihr den ersten Preis zuzuerkennen.
It was an honor for the jury to award her first prize.
In the abstract meaning of ascribing or attributing, the verb is used with qualities or values. Typical objects are 'einen hohen Wert' (a high value), 'eine besondere Bedeutung' (special significance), or 'eine wichtige Rolle' (an important role).
Diesem historischen Ereignis muss man eine große Bedeutung zuerkennen.
One must attribute great significance to this historical event.
to recognize / acknowledge
'anerkennen' and 'zuerkennen' are close in meaning because both can have to do with official evaluation or approval. 'anerkennen' means that you accept something as valid or see the value of an achievement. 'zuerkennen' has a stronger sense of something being granted to someone, for example a right, a prize, or money. It can also mean attributing a quality to someone. The words can be confused especially in official situations. Remember: you 'erkennt etwas an' when you accept it; you 'erkennt jemandem etwas zu' when you award, grant, or ascribe it to that person.

Das Gericht erkennt der Familie eine Entschädigung zu.
The court awards the family compensation.
Frau Meier erkennt die Erfahrung des neuen Mitarbeiters an.
Ms. Meier acknowledges the new employee's experience.