
anfallen
to attack
To suddenly and aggressively physically attack someone or an animal.
Der Hund ist ohne Vorwarnung den Postboten angefallen.
The dog attacked the mail carrier without warning.
to attack / arise / come over
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to attack
To suddenly and aggressively physically attack someone or an animal.
Der Hund ist ohne Vorwarnung den Postboten angefallen.
The dog attacked the mail carrier without warning.

to arise / accrue
To arise as work, costs, or waste and have to be dealt with or managed.
Bei der Renovierung ist viel mehr Müll angefallen als erwartet.
Much more trash arose during the renovation than expected.

to come over
For a feeling or state to suddenly and unexpectedly come over someone.
Plötzlich fiel ihn eine große Müdigkeit an.
A great tiredness suddenly came over him.
'Anfallen' is a separable verb. The prefix 'an-' goes at the end in a main clause. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Der Hund fällt den Briefträger an.
The dog attacks the mail carrier.
You can recognize the meaning from the subject: if a living being attacks, it refers to an attack. If the subject is something abstract like 'Kosten' (costs) or 'Arbeit' (work), it means 'to arise'. If the subject is a feeling, it means 'to come over'.
Der Löwe fällt seine Beute an.
The lion attacks its prey.
In the meaning 'entstehen' (to arise), 'anfallen' is almost always used for impersonal things. Typical examples are costs, fees, work, trash, or data.
Bitte entsorgen Sie den Müll, der bei der Feier angefallen ist.
Please dispose of the trash that was generated during the party.
When a feeling comes over someone, the feeling is the subject and the person is the accusative object. So the sentence structure is: [feeling] fällt [person] an.
Mitten im Gespräch fiel sie eine plötzliche Angst an.
In the middle of the conversation, a sudden fear came over her.
to arise
Both words can say that something new is added as a result of a process. „Entstehen“ generally describes something being formed, whereas „anfallen“ is especially typical of work, costs, or waste that subsequently has to be dealt with. „Anfallen“ is usually the better choice for such quantities or burdens.

Beim Umbau des Hauses fiel viel Bauschutt an.
A lot of construction debris accumulated during the renovation of the house.
Beim Umbau des Hauses entstand viel Staub.
A lot of dust was created while the house was being renovated.